Quail Mountain is the highest peak within the Joshua Tree National Park. While the park is well known for its hundreds of climbing routes amid the towering exposed rock and slabs, many fine backcountry hiking routes exist, many of them very lightly traveled. Quail Mountain is visible from along the main park road, rising off to the southwest as one enters into the park from the north (see the hiking route for more detailed information). There are no developed trails to the summit, thus offering moderately challenging navigation, although no technical gear or skill is required if you choose your route wisely. Surprisingly few people visit the summit; you stand a very good chance of having the peak and the range to yourself, even during the busy winter season.
Quail Mountain is one of the 140+ peaks in California with at least 2,000 feet of prominence. It ranks at #117 on the list, but the prom-chasers will probably be eyeballing this peak nevertheless. It is also a popular HPS destination. It's an all-around fun hike no matter your reasons for climbing it.
From CA-62 in the town of Joshua Tree (roughly 120 miles east of Los Angeles and about 45 miles from the junction of CA-62 and Interstate-10 near Palm Springs), follow the main park road south into the National Park. It's extremely well signed and you cannot miss it. Pay your fee and proceed. Drive southeasterly along this main park road to a pull out on your left, about 7.7 miles from CA-62, very near a massive rock outcrop. See the hiking route page for more detailed information, including topozone links to the appropriate location. Quail Mountain is visible to your right (southwest), about 3.8 air-miles away. It is in every way a classic desert peak.
An entrance fee is required for the park. Please see the link below for full details about JTNP.
Summer can be extremely hot. The whole route is remote and off the beaten path. Generally conditions from October through April are best. Snow is rare and shouldn't linger, and most winter days are dry and temperatures in the 70s.
Camping is available in the park as well as outside the park. See the link below for further information. The town of Joshua Tree along CA-62 has some basic hotels. Nearby cities Twentynine Palms and Yucca Valley also have lodging.
Generally, the areas along highway CA-62 from the north (29 Palms, Joshua Tree (town), Yucca Valley) are built-up enough to make scatter-camping unattractive. From the south entrance (from I-10 east of Indio), you are in wide-open desert, and if you absolutely must scatter-camp for the monetary and spiritual aspects, I am sure you can find a spot off the main roads without trouble. It's desert, so shade trees are few. The land outside the park and away from the cities is mostly BLM.
I'd vote to camp within the park.
This is the canonical Joshua Tree National Park link:
Joshua Tree Information Page
90% of visitors enter the park from the north, but the main park road exits to the southeast at Interstate-10 in the middle of nowhere, about 30 miles east of Indio. If coming from the east, this would be a good place to enter the park - take the obvious "Joshua Tree National Park" exit (also signed for the town of Mecca). I don't recall the mileage to the trailhead area from this exit, but it's about an hour's drive. This road is a popular driving route, as it transitions from the high desert part of the park (with all the joshua trees) down to the lower, harsher parts of the park (featuring expansive gardens of cholla cactus).
The cities of Indio and Coachella have the closest extensive services. If gas is all you need, you can stop at Chiriaco Summit which is about 10 miles west of the JTNP exit off of I-10. Chiriaco Summit isn't a town in the real sense but it does host the General Patton museum. The community of Desert Center (about 30 miles east of the JTNP exit) offers very limited services. It's a dumpy place that has seen better days (it was a major stop back when I-10 was not yet built and US-60 was the main thoroughfare between SoCal and Phoenix. Some of old US-60 still fronts I-10 for many miles in the area).